Related papers: Level-crossing distributions of kinematic variable…
The influence of forward speed on stochastic free-surface crossing, in a Gaussian wave field, is investigated. The case of a material point moving with a constant forward speed is considered; the wave field is assumed stationary in time,…
A stochastic second-order wave model is applied to assess the statistical properties of wave orbital velocity in random sea states below the water surface. Directional spreading effects as well as the dependency of the water depth are…
In applications spaning from image analysis and speech recognition, to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a…
Let $X=\{X_t: t\ge 0\}$ be a stationary piecewise continuous $\R^d$-valued process that moves between jumps along the integral curves of a given continuous vector field, and let $S\subset\R^d$ be a smooth surface. The aim of this paper is…
We address the counting of level crossings for inertial stochastic processes. We review Rice's approach to the problem and generalize the classical Rice formula to include all Gaussian processes in their most general form. We apply the…
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…
The evolution of crossing sea states and the emergence of rogue waves in such systems are studied via numerical simulations performed using a higher order spectral method to solve the free surface Euler equations with a flat bottom. Two…
Sinking marine snow particles, composed primarily of organic matter, control the global export of photosynthetically fixed carbon from the ocean surface to depth. The fate of sedimenting marine snow particles is in part regulated by their…
This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their…
The notion of multivariate upcrossings index of a stationary sequence ${\bf{X}}=\{(X_{n,1},\ldots,X_{n,d})\}_{n\geq 1}$ is introduced and its main properties are derived, namely the relations with the multivariate extremal index and the…
We use Rice formulae in order to compute the moments of some level functionals which are linked to problems in oceanography and optics: the number of specular points in one and two dimensions, the distribution of the normal angle of level…
We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. We study…
We use Rice's formulas in order to compute the moments of some level functionals which are linked to problems in oceanography and optics. For instance, we consider the number of specular points in one or two dimensions, the number of…
When the unconditioned process is a diffusion submitted to a space-dependent killing rate $k(\vec x)$, various conditioning constraints can be imposed for a finite time horizon $T$. We first analyze the conditioned process when one imposes…
The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
The aim of this study is to extend the scope and applicability of the level-crossing method to discrete-time stochastic processes and generalize it to enable us to study multiple discrete-time stochastic processes. In previous versions of…
The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and…
The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control…